The field of the invention is nuclear magnetic resonance imaging methods and systems. More particularly, the invention relates to the correction of image artifacts caused by "Maxwell terms" produced by MRI systems.
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B.sub.0), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B.sub.1) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, M.sub.z, may be rotated, or "tipped", into the x-y plane to produce a net transverse magnetic moment M.sub.t. A signal is emitted by the excited spins, and after the excitation signal B.sub.1 is terminated, this signal may be received and processed to form an image.
When utilizing these signals to produce images, magnetic field gradients (G.sub.x, G.sub.y, and G.sub.z) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received NMR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
It is well known that imperfections in the linear magnetic field gradients (G.sub.x, G.sub.y, and G.sub.z) produce artifacts in the reconstructed images. It is a well known problem, for example, that eddy currents produced by gradient pulses will distort the gradient fields and produce image artifacts. Methods for compensating for such eddy current errors are also well known as disclosed, for example, in U.S. Pat. Nos. 4,698,591; 4,950,994; and 5,226,418.
It is also well known that the gradients may not be perfectly uniform over the entire imaging volume, which may lead to image distortion. Methods for compensating this non-uniformity are described, for example, in U.S. Pat. No. 4,591,789.
Other than uncompensated eddy current errors and gradient non-uniformity errors that escape correction, it can be assumed that the magnetic field gradients (G.sub.x, G.sub.y, and G.sub.z) produce linear magnetic fields exactly as programmed, thus spatially encoding the NMR data accurately. With these gradients, the overall static magnetic field at location (x,y,z) is conventionally given as B.sub.0 +G.sub.x x+G.sub.y y+G.sub.z z, and the direction of the field is usually thought to be along the z-axis. This description, however, is not exactly correct. As long as a linear magnetic field gradient is applied, the overall magnetic field is nutated away from the z-axis and its amplitude exhibits higher-order spatial dependencies (x.sup.2, y.sup.2, z.sup.2, z.sup.3, . . . ). These phenomena are a direct consequence of the Maxwell equations which require that the overall magnetic field satisfy the following two condition: .gradient..multidot.B=0 and .gradient..times.B=0. The higher-order magnetic fields, referred to as "Maxwell terms" (or Maxwell fields), represent a fundamental physics effect, and are not related to eddy currents or imperfection in hardware design and manufacture. Although Maxwell terms have been known for at least a decade, their effect on imaging has been largely ignored because of their minute consequences for conventional imaging conditions.
Echo-planar imaging ("EPI") is one of the ultrafast MR imaging techniques that has many clinical applications. Consider, for example, a superconducting MRI system where the main magnetic field is oriented along the long axis of the patient. EPI can then suffer from severe image distortion when the imaged slice is oriented in a sagittal or coronal plane and frequency or phase encoding is performed along the direction of the polarizing magnetic field B.sub.0. In addition, there is a certain amount of ghosting and blurring in such images. The image distortion, ghosting, and blurring in such images are caused by the Maxwell terms. As a result, EPI has been usually limited in both clinical and research applications to axially oriented slices which are perpendicular to the magnetic field B.sub.0.